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MODELLING SOIL PORE WATER PRESSURE USING SIGMOID KERNEL FUNCTION
NURUL SYAHIRAH BINTI KAMARUL BAHRIN
CIVIL AND ENVIRONMENTAL ENGINEERING
UNIVERSITI TEKNOLOGI PETRONAS
SEPTEMBER 2016
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Modelling Pore Water Pressure Using Sigmoid Kernel Function
by
Nurul Syahirah binti Kamarul Bahrin
17433
Dissertation submitted in partial fulfilment of
the requirements for the
Bachelor of Engineering (Hons)
(Civil and Environmental Engineering)
SEPTEMBER 2016
Universiti Teknologi PETRONAS,
32610, Bandar Seri Iskandar,
Perak Darul Ridzuan
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CERTIFICATION OF APPROVAL
Modelling Pore Water Pressure Using Sigmoid Kernel Function
by
Nurul Syahirah binti Kamarul Bahrin
17433
A project dissertation submitted to the
Civil and Environmental Engineering Programme
Universiti Teknologi PETRONAS
in partial fulfilment of the requirement for the
BACHELOR OF ENGINEERING (Hons)
(CIVIL AND ENVIRONMENTAL ENGINEERING)
Approved by,
_____________________
(Dr Muhammad Raza Ul Mustafa)
UNIVERSITI TEKNOLOGI PETRONAS
BANDAR SERI ISKANDAR, PERAK
September 2016
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CERTIFICATION OF ORIGINALITY
This is to certify that I am responsible for the work submitted in this project, that the
original work is my own except as specified in the references and
acknowledgements, and that the original work contained herein have not been
undertaken or done by unspecified sources or persons.
________________
NURUL SYAHIRAH BINTI KAMARUL BAHRIN
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ABSTRACT
Pore-Water Pressure (PWP) is an influential parameter for monitoring slope
stability responses to rainfall especially in the area that prone to experience slope
failure. Monitoring PWP that is in the form of nonlinear complex data however is
expensive and require quite tedious task through traditional approach for evaluation
purposes. In respond to that, recently, PWP able to be modelled by soft computing
techniques - Support Vector Machine (SVM). SVM will determine the optimal linear
separating plane in high dimension feature space of nonlinear complex data by its
numerous kernel function technique. The data on rainfall is collected at slope site of
Universiti Teknologi PETRONAS, Perak. The study is merely to predict PWP
fluctuations occur based on the rainfall event at instrumented slope by developing two
SVM model using Sigmoid Kernel Function technique. The model is then evaluated
by coefficient of determination (R2) and mean square error (MSE) to obtain optimum
meta-parameters. Model 1 shows a better result in term R2 and MSE compared to
Model 2 by 20.3%. The study successfully demonstrated Sigmoid Kernel Function
model is effective to predict accurate PWP and can be applied in any slope
management studies.
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ACKNOWLEDGEMENTS
I would like to express the deepest appreciation to my supervisor, Dr Muhammad Raza
Ul Mustafa, who continually and convincingly conveyed a spirit of adventure in regard
to research and an excitement in regard to teaching. In addition, a thank you to Mr
Nuraddeen Muhammad Babangida who introduced me to soft computing technique,
Support Vector Machine (SVM). Without his guidance and persistent help, this
dissertation would not have been possible.
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TABLE OF CONTENTS
CERTIFICATION OF APPROVAL I
CERTIFICATION OF ORIGINALITY II
ABSTRACT III
ACKNOWLEDGEMENTS IV
LIST OF FIGURES VII
LIST OF TABLES VIII
LIST OF EQUATIONS IX
CHAPTER 1: INTRODUCTION 1
1.1 Project Background 1
1.2 Problem Statement 2
1.3 Objectives 3
1.4 Scope of study 3
CHAPTER 2: LITERATURE REVIEW 4
CHAPTER 3: METHODOLOGY/PROJECT WORK 8
3.1 Study area 8
3.2 Instrument and Data Source 10
3.2.1 Tensiometers 10
3.2.2 Tipping Bucket Rain Gauge 11
3.3 Support Vector Machines 12
3.4 Sigmoid Kernel Function 13
3.5 Support Vector Regression Model 14
3.6 Development of Sigmoid Kernel Function Model 15
3.7 Gantt chart 16
3.8 Key Milestone 18
CHAPTER 4: RESULT AND DISCUSSION 19
4.1 Data Analysis 19
4.2 Normalization of data 23
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4.3 Model Input Structure 24
4.4 Implementation of SVR 26
4.5 Performance Measure 27
4.6 Results and Discussion 27
4.6.1 Model 1 Result Analysis and Discussion 31
CONCLUSION AND RECOMMENDATION 34
REFERENCES 35
APPENDICES 38
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List of Figures Figure 1: Simple block diagram of neuron ................................................................4
Figure 2: Applications of Support Vector Machine ...................................................6
Figure 3: Location of the study area ..........................................................................8
Figure 4: Location of tensiometers and tipping bucket rain gauge at study area .........9
Figure 5: Tensiometers ........................................................................................... 10
Figure 6: Tipping bucket rain gauge ........................................................................ 11
Figure 7: Tipping bucket rain gauge information ..................................................... 11
Figure 8: Sigmoid Kernel Function Model development ......................................... 15
Figure 9: Key Milestone ......................................................................................... 18
Figure 10: PWP Graph ............................................................................................ 20
Figure 11: Rainfall Graph ....................................................................................... 21
Figure 12: Pore Water Pressure, Predicted Pore Water Pressure and Rainfall Graph 31
Figure 13: Extent of agreement between observed and predicted PWP records........ 33
Figure 14: Codes used in MATLAB software ......................................................... 38
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List of Tables Table 1: FYP1 Gantt Chart ..................................................................................... 16
Table 2: FYP2 Gantt Chart ..................................................................................... 17
Table 3: Data Analysis ............................................................................................ 19
Table 4: Number of data points for training and testing .......................................... 22
Table 5: Input Paramaters ....................................................................................... 26
Table 6: Model 1 trial and error input for parameters value ..................................... 28
Table 7: Model 2 trial and error input for parameters value ..................................... 29
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List of Equations Equation 1: Equation of hyperplane ........................................................................ 12
Equation 2: SVM training vector............................................................................. 13
Equation 3: Sigmoid Kernel Function ..................................................................... 13
Equation 4: MSE .................................................................................................... 14
Equation 5: R-squared............................................................................................. 14
Equation 6: Normalization of data ........................................................................... 23
Equation 7: Antecedent formula 1 ........................................................................... 24
Equation 8: Antecedent formula 2 ........................................................................... 24
Equation 9: Antecedent formula 3 ........................................................................... 25
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CHAPTER 1
INTRODUCTION
1.1 Project Background
Pore Water Pressure (PWP) as in general, is the indicator of the existence of
water filled the voids that exert external forces within the soil. This is influenced by
either the physical location of the soil or other natural factor like rainfall that results in
fluctuation of PWP reading. The presence of the water resulting the soil to become
more saturated that relates to the pressure difference within the soil. This can be
illustrated by the parameter of pressure readings, buoyancy effect and shear strength
of the soil. Zero reading of PWP indicates the soil voids are filled with air, negative
reading of PWP indicates the soil voids are partly filled with the water while positive
reading of PWP is when the soil voids are fully filled with the water. Varies in reading
of PWP affects in the shear strength of the soil. The saturated state of the soil has
achieved buoyancy effect and thus, reflects to the reducing shear strength in the soil.
In fact, shear resistance is proportionally depending on the shear strength of the soil.
Therefore, the reduction in shear resisting capacity of the soil due to the increase of
PWP and decrease of the shear strength is unfavourable. This is because the reduction
of shear resisting capacity of the soil will cause slope failure and leads to landslides.
Hence, in hydrological perspectives, knowledge on PWP is vital in order to study
seepage analyses, forecast possible failures on the slope, design slope and evaluates
the slope responses to rainfall.
Previous studies had been conducted to model and predict PWP by using data-
driven models on artificial intelligence. Most past studies showed artificial neural
network (ANN) had successful demonstrate PWP modelling. Nonetheless, recently,
support vector machines (SVM) had been noticed to perform as well as ANN. This
study is going to prove on how Sigmoid kernel function (one of SVM’s techniques)
can be used to predict and model PWP.
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1.2 Problem Statement
Rainfall often notably as one of the factors that weakens the earth slope. It can
be found by number of ways and the way it increases saturation’s degree of soil thus
loosen the bonds of the surface tension between the particles of the soil (Borja &
White, 2010). Borja and White (2010) also stated that if the volume of water infiltrates
is large enough, the degree of saturation of the soil increases and thus able to produce
downhill frictional drag on the slope. The increase degree of saturation in the soil affect
the excess volume of water that can no longer infiltrate into the slope and then
discharged as surface runoff that caused the slope erodibility.
The implications of slope instability can be widely seen through landslides
tragedy all over the world. Landslides that occurred from the past decades back in 1982
until recently 2006 had documented numbers of fatalities and severe destruction.
Massive rainfall and the preparedness to it diagnosed as the primary factor of the
landslides event. Due to that, studies related to seepage analyses, slope stability
analyses, engineered slope design and evaluating slope responses to rainfall is needed.
PWP is the element that contribute to the studies as it can demonstrate both predicting
and modelling of rainfall.
Past studies had successful practiced neural networks as a tool to predict PWP
responses to rainfall. However, recently, support vector machine (SVM) has the same
ability as neural networks to be used for similar purposes. Sigmoid kernel function is
one of the techniques falls under SVM and is going to be introduced in this research
to prove on how effective it is to predict and model variation responses of rainfall.
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1.3 Objectives
The objectives of this research that is prediction of pore water pressure
responses to rainfall are as follows;
• To predict pore water pressure responses to rainfall using Sigmoid
Kernel function.
• To evaluate the model performance by using statistical measures.
1.4 Scope of study
The scope of this research will focus on;
• The application of Sigmoid kernel function for modelling pore water
pressure responses to rainfall using Matlab software.
• The performance of the model using coefficient of determination (R2)
and mean square error (MSE).
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CHAPTER 2
LITERATURE REVIEW
Numerous past studies had come out with the same idea of pore water pressure
has significant impact on the slope stability through the evaluation effect of the
increase in pore water pressure on the stability of the slope (Yoshinaka et al., 1997;
Furuya et al., 2006; Matsuura et al., 2008; Huang et al., 2012). Mustafa et al. (2012)
has stated that the increase in pore water pressure contribute to the reducing shear
strength of soil and thus caused slope failures. Further studies then conducted to prove
the statement by various type of approaches and techniques.
The data to be used in the study however consist of complex relationships.
Data-model driven on artificial intelligence able to demonstrate the complex
relationship in model manner. Artificial Neural Networks (ANNs) is one of the
approaches falls under artificial intelligence that works just as human nervous systems
that consists of neurons (illustrated as below).
Figure 1: Simple block diagram of neuron
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ANN had been successful widely used in various field of engineering including
geotechnical (Mustafa et al., 2012). Goh (1995) had a research in providing the
estimation of maximum wall deflection for braced excavations by developing a neural
network model (Tarawneh, 2016). Kahraman (2005) introduced multi-layered
perception (MLP) approach in ANN to determine the prediction of carbonate rocks
saw ability through shear strength parameters. Kaunda (2014) demonstrated on how
different rock types examined through ANN simulations and the responses to principal
stress effects. Momeni et al. (2015) presented the utilization of particle swarm
optimization in order to predict unconfined compressive strength of the rocks by
modelling ANN. In hydrology aspect, there are several studies that had successful use
the application of ANN in predicting quality of water (May and Sivakumar 2009) and
forecast of river flow (Dibike and Solomatine 2001).
There are researches done (Mustafa et al. 2010, 2012, 2013) to predict pore
water pressure using the same application of ANN. In the research, the prediction using
ANN is being tested by different techniques of scaled conjugate gradient (SCG)
learning algorithm, radial basis function neural network (RBFNN) and multilayer
perceptron. The outcome of the research by SCG learning algorithm is applicable to
be used to predict non-linear behaviour as variation of pore water pressure during
rainfall event. While RBFNN modelling has slight lacking of the ability to explain
functional relationships between variables, it does have the advantage of using limited
number of parameters. Whereas multilayer perception technique indicated the during
both training and testing with gradient descent (GD), gradient descent with momentum
(GDM), SCG and Levenberg-Marquardt (LM) algorithm, LM is identified as the
ultimate training algorithm as least time and minimum error obtained for soil pore
water pressure.
Recently, support vector machine (SVM) that is another artificial intelligence
component, had gained vast attention from researchers for its ability to utilize linear
function in a high dimensional feature space. Various researches that used SVM
approach which introduced by Vapnik and others in early of 1990s, have achieved a
successful outcome especially in hydrological field of study for example study carried
out by Lin et al. (2013) using SVM approach to forecast typhoon flood. In the study,
a two-stage SVM-based model is developed to yield 1-to 6-h lead time runoff
forecasts. The model developed is undergone pre-process the information of typhoon
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and then forecasting the rainfall. The rainfall data is set as an input data to predict the
flood module. Tehrany et al. (2014) also use SVM approach to map flood susceptibility
in GIS. The data validated by SVM parameter indicate the proposed method improved
flood modelling by 29%. Shrestha and Shukla (2015) has study on the
evapotranspiration using hydro-climatic variables with SVM approach. They
discovered SVM model is performing better and more accurate compared ANN and
Relevance Vector Machine. Research done by Kundu et al. (2016) using Least Square
(LS) technique of SVM model to study the future changes in rainfall, temperature and
reference evapotranspiration in the central India. The model is evaluated based on its
efficiency by different statistical method.
Other than research stated, SVM has contributed in many more as in following
figure;
Figure 2: Applications of Support Vector Machine
SUPPORT VECTOR
MACHINE
Application in field of Surface
Water Hydrology
Rainfall-runoff forecasting
Streamflow and sediment yield forecasting
Evaporation & evapotranspiration
forecasting
Flood forecasting & drought forecasting
Application in the field of Ground
Water Hydrology
Ground water level prediction
Soil moisture estimation
Ground water quality assessment
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N and Deka (2013) stated the contribution of SVM in hydrology aspects has
been in significant number due to its promising and reliable analysis through series of
development. SVM has given insight to be successful in classification problems,
regression and forecasting through its machine learning techniques. Due to that,
Babangida et. al (2016) has come out with the idea of using SVM approach to predict
pore water pressure response to rainfall. Support vector regression technique is being
used for modelling the data responses to rainfall and has proven show good results
compared to their previous study using ANN. Based on its performance, the same
SVM approach but with different technique of Sigmoid kernel function is going to be
used in this study to evaluate on the performance of the pore water pressure prediction
since there is no study focusing on it being done yet.
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CHAPTER 3
METHODOLOGY/PROJECT WORK
This chapter illustrate methodology of the project that covers for study area,
instruments used, data source and modelling process.
3.1 Study area
Study area for this project is located on the selected slope within the grounds
of Universiti Teknologi PETRONAS that close to Block 5. The selected soil slope is
about 11 m high. Following figures show location of this project.
Figure 3: Location of the study area
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Figure 4: Location of tensiometers and tipping bucket rain gauge at study area
Slope variables are vital to be used in this project. Following are the parameters
for site detail and soil properties of the slope;
1. Slope properties
§ Area
§ Slope angle
§ Slope height
§ Topography
2. Soil engineering properties
§ Water content
§ Liquid limit
§ Plastic limit
§ Effective cohesion
§ Soil type
§ Angle of friction
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3.2 Instrument and Data Source
3.2.1 Tensiometers
Figure 5: Tensiometers
Measuring devices to be used in this project are tensiometers. The primary
function of tensiometers are to obtain soil water contain from the rainfall. The
tensiometers is installed in the depth of 0.6 m.
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3.2.2 Tipping Bucket Rain Gauge
Figure 6: Tipping bucket rain gauge
Figure 7: Tipping bucket rain gauge information
Tipping Bucket Rain Gauge is primarily functioning to evaluate the rainfall. It
comprises of a funnel that collects the rainfall then channelled it to the metallic tipping
bucket measuring system. Then reed switch will detect when the bucket has tipped and
produces a momentary contact closure signal. The cycle keeps continue as long as the
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rainfall continues to fall. The rainfall gauge then will connect to a data logger as it
detected and recorded the data through a counter channel. The time interval set is 30
minutes.
3.3 Support Vector Machines
As stated by Babangida et. al. (2016), Support Vector Machines (SVM) is
being discovered as a reliable soft computing method that promotes method of learning
classification, interpolation, functional estimation and etc. (Kecman, 2001).
SVM govern discriminative classifier that defined by separating hyperplane.
The operation in SVM algorithm enable to find the largest minimum distance of
hyperplane so that the hyperplane will not cause noise in the data and thus affect the
generalization of data. The equation of hyperplane is as following;
Equation 1: Equation of hyperplane
f(x) = x′β + b =0 (1)
where β ∊ Rd and b is a real number.
By introducing this SVM approach, it is enables the use of linear classifiers as
solutions for nonlinear problems for example pore water pressure data prediction.
Nonlinear transformation also can be illustrated by various techniques of Kernels such
as polynomials, radial basis function, multilayer perception (neural network), Sigmoid
kernel function and etc. In order to supervised learning model, SVM need to undergone
process of training, classifying and tuning. SVM approach will use Support Vector
Regression as the model implementation and Sigmoid kernel function as the technique
to implement and thus evaluate the model.
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3.4 Sigmoid Kernel Function
Sigmoid kernel function or also known as Hyperbolic Tangent Kernel has been
chosen to model pore water pressure. The kernel training vectors involved in this study
derived from SVM training vector which is as follows;
Equation 2: SVM training vector
(2)
While for Sigmoid kernel function vector is as follows;
Equation 3: Sigmoid Kernel Function
k (x, y) = tanh (γxTy + r) (3)
Based on the training vector, SVM model using sigmoid kernel function is
equivalent to a two-layer, perceptron neural network. Therefore, the result originated
from Sigmoid kernel function will then compared to predicted values in identifying
the performance of the model and the factor contributes to the variance of the result.
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3.5 Support Vector Regression Model
Support Vector Regression (SVR) is used as evaluator in the process of
developing the model. Mean Square Error (MSE) being used to measure model
accuracy. This can be shown by following formula;
Equation 4: MSE
𝑀𝑆𝐸 = &'∑ )Ŷ − 𝑌-.''/& (4)
Low values of MSE are desirable as indicator to get how close the model
predictions with observed values. Coefficient of determination (R2) with the high value
is desirable in demonstrating the unity value that shows the strength relationship
between model predictions and observed values. This can be shown as in following
formula;
Equation 5: R-squared
R2 = ∑(12ū)52∑(û21)5
∑(12ū)5 (5)
The kernel function selected, as for this case, Sigmoid kernel function, then
will be used in model implementation along with other parameters of regularization
parameter, C and width of corridor minimized by SVM, ε. This is done by trial and
error method in order to determine most reliable values for respective parameters.
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3.6 Development of Sigmoid Kernel Function Model
Figure 8: Sigmoid Kernel Function Model development
Site Visit
Problem Analysis, Data Gathering and Data Pre-
processing
Development of Model using Matlab software
Model Analysis (Training and Validation) & Evaluation
Conclusion & Report Submission
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3.7 Gantt chart
A total of 14 weeks are given to complete this project. Gantt charts for Final
Year Project 1 & 2 are stated below;
Table 1: FYP1 Gantt Chart
Week
Details
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Selection of Project Title
Preliminary Research
Work
Submission of Extended
Proposal
Proposal Defence
Project work continues
Submission of Interim
Draft Report
Submission of Final
Interim Report
Deadline
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Table 2: FYP2 Gantt Chart
Week
Details
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Project Work Continues
Submission of Progress
Report
Project Work Continues
Pre-SEDEX
Submission of Draft
Final Report
Submission of
Dissertation (soft
bound)
Submission of Technical
Paper
Viva
Submission of Project
Dissertation (Hard
Bound)
Deadline
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3.8 Key Milestone
JuneSelection
project title and
preliminary work
JulySubmission
extended proposal
and proposal defence
AugustSite visit and data
collecting
SeptemberData
processing and data analysis
OctoberModel
implementation using Sigmod
Kernel Function
NovemberPerformance
measure
DecemberResult and discussion
Figure 9: Key Milestone
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CHAPTER 4
RESULT AND DISCUSSION
This chapter illustrated model development of support vector machine. Model
development of support vector machine need particular consideration in determining
its input combination and right meta-parameters. This is including the analysis of data.
4.1 Data Analysis
An entirely month of data in November 2014 is selected in this study. A total
of 1440 of data points for pore water pressure (PWP) and rainfall respectively used in
this study. All data points need to be divided into training and testing datasets in order
to model the prediction of PWP with a better accuracy. The selection of both training
and testing datasets are according to the data analysis with the breakdown of 70% for
training and 30% for testing that has been successfully practiced through past studies
by Mustafa et al. (2012), Rahardjo et. al. (2008) and Babangida et. al. (2016).
Following is the preliminary data analysis;
Table 3: Data Analysis
The maximum, minimum and mean of PWP data points show negative value
which means the slope is not experiencing low slope stability. Same goes to rainfall
data points, with its minimum value of zero and maximum value of 30.5, the mean of
data points is 0.171 which means the frequency of the slope experiencing and receiving
rain events are not continuously same throughout the entire month. Same goes to the
skewness of the data points, PWP experiencing positive skewness and rainfall
experiencing negative skewness respectively.
Data statistics PWP Rainfall Number (N) 1440 1440 Mean -8.787 0.171 Standard Deviation 1.174 1.424 Min -11.5 0 Max -4.9 30.5 Skewness 0.376 13.909
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The graph of both PWP and rainfall are illustrated as following;
Figure 10: PWP Graph
-12
-11
-10
-9
-8
-7
-6
-5
11/1/2014 11/6/2014 11/11/2014 11/16/2014 11/21/2014 11/26/2014
PWP
(kpa
)
Time (30-mins interval)
PWP GraphPWP
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Figure 11: Rainfall Graph
Based on the graphs above, it shows that most and maximum data points for
both PWP and rainfall falls towards the end of month. Hence, it is preferable to select
the training datasets starting from 10th November till 30th November 2014 in order to
train the datasets with the worst case of data points and ease the testing process to take
place. Whilst testing datasets are selected starting from 1st November till 9th November
2014.
However, to validate the effectiveness and accuracy of aiming selected
datasets, it will be compared with the different selection of training and testing
datasets. The training datasets are selected from the beginning of November to 22nd
November of 2014 whereas testing datasets are selected from 22 November to the end
of November 2014.
The model is labelled as Model 1 and Model 2 to represent two different
selection of datasets respectively. Model 1 is representing training datasets from 10th
0
5
10
15
20
25
30
11/1/2014 11/6/2014 11/11/2014 11/16/2014 11/21/2014 11/26/2014
Rain
fall
(mm
)
Time (30 min interval)
Rainfall Graph
Rainfall
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November till 30th November 2014 while Model 2 is represent training datasets from
beginning of November till 22nd November 2014.
Table 4: Number of data points for training and testing
Model 1 Model 2
Training Testing Training Testing
Date of data
points
10th November –
30th November
2014
1st November –
10th November
2014
1st November –
22nd November
2014
22nd November –
30th November
2014
Number of
data points 1008 432 1008 432
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4.2 Normalization of data
However, the datasets are consisting of large variance from one points to
another. This can be illustrated by the standard deviation in data analysis. Both
maximum and minimum value for PWP and rainfall are having larger value from its
standard deviation which tells us some of data points are experiencing both extra small
and extra large value.
Thus, to close the large gap between the data points, it is better to normalize
the data points into a smaller range of value. In this study, the range of -1 to 1 is
selected according to following equation;
Equation 6: Normalization of data
𝑣8/2x(
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4.3 Model Input Structure
According to Babangida et al. (2016), it is important to focus in model input
structure as varies in selected inputs data will result significant rise to different model
and affect the model accuracy. This has been proved through the studies done by
Mustafa et al. (2012) and Rahardjo et al. (2008) that adopted different numbers of
present and antecedent for both rainfall and PWP. The adoption of antecedent rainfall
events will result sharp rise in PWP due to its enough total rainfall. However,
antecedent rainfall itself is not enough to provide a good prediction. Hence, antecedent
PWP also needed to enhance a good prediction of PWP (Babangida et al., 2016).
The input features as stated by Babangida et al. (2016) are established by using
detailed cross correlation analysis between PWP and rainfall as well as auto correlation
analysis of PWP. Following is the input patterns used by Mustafa et al. (2012) in
equation 6 and Rahardjo et al. (2008) in equation 7.
Equation 7: Antecedent formula 1
Ut = fSVR (U(t-1, …., t-5), r(t, t-1, t-2)) (7)
Equation 8: Antecedent formula 2
Ut = fSVR (U(t-1, t-2), r(t, t-1, …., t-5)) (8)
Where
t = time index of the order of 30 min
Ut-n = PWP at any time t-n
rt-n = rainfall at any time t-n
fSVR = model type
The latest study by Babangida et al. (2016) found that, the limitation used of
input features for both antecedent rainfall and PWP record gives better result.
Due to that, the study has come out with the following optimum input patterns
that give increase in accuracy;
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Equation 9: Antecedent formula 3
Ut = fSVR (U(t-1, t-2, t-3), r(t, t-1, t-2)) (9)
Therefore, above input pattern is adopted in this study accordingly.
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4.4 Implementation of SVR
For SVR implementation, sigmoid kernel function is selected based on the
following formula;
k (x, y) = tanh (γxTy + r) (3)
According to Kisi and Cimen (2011) and Lin and Lin (2005), the parameters
selected in the model implementation: cost (C), gamma (γ), epsilon (ε) and coef0 (r).
C parameter is a positive constant capacity control parameter, γ is constant that reduces
model space and controls the solution’s complexity, while ε is loss function that
describes regression vector without all data input whereas r is a shifting parameter that
controls the threshold of mapping. The other input value is t which represent sigmoid
kernel function value.
As stated by Babangida et. al. (2016), all kernel parameters stated above have
to be calibrated according to its default value as following;
Table 5: Input Paramaters
Parameters Value
svm_type (-s) *constant for all training
and testing datasets
Default: 3
kernel_type (-t) *constant for all
training and testing datasets
Default: 3
cost (-c) Default: 1
gamma (γ/-g) Default: 1
epsilon (ε/-p) Default: 0.1
coef0 (-r) Default: 0
The value of -c, -g, -p and -r are adjusted by trial and error method in MATLAB
software with LIBSVM (a library for support vector machines) to obtain best accurate
result based on performance measure as stated below.
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4.5 Performance Measure
The performance measure selected for this study to obtain best accuracy of
prediction are coefficient of determination (R2) that shows the model fits the data (1
indicates perfect fit while 0 indicates poor fit) and mean square error (MSE) where
smaller value approaching to 0 is desirable.
4.6 Results and Discussion
The result of trial and error method for each parameter in the MATLAB
software is as following. There are 20 sets of trial and error method altogether that has
the input values of;
i. 5 sets of constant value of all parameters except gamma, γ
ii. 5 sets of constant value of all parameters except cost constant, c
iii. 5 sets of constant value of all parameters except epsilon, ε
iv. 5 sets of constant value of all parameters except coefθ, r
with the best previous value used for the constant value for each 5 sets respectively.
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Table 6: Model 1 trial and error input for parameters value
SET
Parameters value Performance Result
Type of SVM
(epsilon-SVR), s
Type of kernel
function (Sigmoid),
t
Cost constant,
c
Gamma, γ
Epsilon, ε
Coefθ, r
R2
(Good = 1)
MSE
(Good = 0)
Number of support
vector, nSV
1 3 3 1 0.01 0.001 -1 0.92894 0.008552 998
2 3 3 1 1 0.001 -1 0.0900857 206.067 1008
3 3 3 1 2 0.001 -1 0.04055 159.257 1008
4 3 3 1 0.001 0.001 -1 0.916125 0.08964 1002
5 3 3 1 0.1 0.001 -1 0.949332 0.005034 990
6 3 3 0.1 0.1 0.001 -1 0.936045 0.00694 986
7 3 3 0.01 0.1 0.001 -1 0.922561 0.065383 1006
8 3 3 0.001 0.1 0.001 -1 0.92089 0.145665 996
9 3 3 2 0.1 0.001 -1 0.949235 0.004973 980
10 3 3 3 0.1 0.001 -1 0.949026 0.004994 963
11 3 3 3 0.1 0.01 -1 0.948979 0.005087 842
12 3 3 3 0.1 0.1 -1 0.950101 0.006006 294
13 3 3 3 0.1 1 -1 -1.#IND 0.232013 0
14 3 3 3 0.1 0.0001 -1 0.949026 0.004998 1004
15 3 3 3 0.1 0.02 -1 0.948647 0.005289 670
16 3 3 3 0.1 0.01 -2 0.948474 0.005208 845
17 3 3 3 0.1 0.01 -0.1 0.592007 0.659466 993
18 3 3 3 0.1 0.01 -3 0.935515 0.007291 883
19 3 3 3 0.1 0.01 -0.03 0.536383 1.13164 997
20 3 3 3 0.1 0.01 -1.5 0.949127 0.005113 847
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Table 7: Model 2 trial and error input for parameters value
SET
Parameters value Performance Result
Type of SVM
(epsilon-SVR), s
Type of kernel
function (Sigmoid),
t
Cost constant,
c
Gamma, γ
Epsilon, ε
Coefθ, r
R2
(Good = 1)
MSE
(Good = 0)
Number of support
vector, nSV
1 3 3 1 0.1 0.001 -1 0.786142 0.032367 943
2 3 3 1 1 0.001 -1 0.105182 340.557 1006
3 3 3 1 2 0.001 -1 0.000727 516.759 1008
4 3 3 1 0.001 0.001 -1 0.689069 0.111573 1008
5 3 3 1 0.01 0.001 -1 0.716055 0.042707 1001
6 3 3 0.1 0.1 0.001 -1 0.731194 0.040295 986
7 3 3 0.01 0.1 0.001 -1 0.698654 0.085452 1006
8 3 3 0.001 0.1 0.001 -1 0.696611 0.175099 1002
9 3 3 2 0.1 0.001 -1 0.788679 0.032358 882
10 3 3 3 0.1 0.001 -1 0.788794 0.032442 880
11 3 3 3 0.1 0.01 -1 0.789002 0.031952 685
12 3 3 3 0.1 0.1 -1 0.781272 0.032642 197
13 3 3 3 0.1 1 -1 5.72E-17 0.151547 0
14 3 3 3 0.1 0.0001 -1 0.788881 0.032561 986
15 3 3 3 0.1 0.02 -1 0.787915 0.032047 551
16 3 3 3 0.1 0.01 -2 0.780316 0.032927 703
17 3 3 3 0.1 0.01 -0.1 0.001726 0.740202 989
18 3 3 3 0.1 0.01 -3 0.728064 0.040657 791
19 3 3 3 0.1 0.01 -0.03 0.032184 1.29113 993
20 3 3 3 0.1 0.01 -1.5 0.786132 0.032243 689
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Based on overall results, set number 5 for Model 1 and set number 11 for Model 2
show the most optimum result according to its performance result of R2 and MSE that
most approaching to 1 and 0 respectively.
Model 1 resulted 0.949332 and 0.005034 for R2 and MSE respectively. While
Model 2 resulted 0.789002 and 0.031952 for R2 and MSE respectively. This can be
concluded that Model 1 is having the most optimum result compared to Model 2 due
to the variance of the rainfall and PWP data used for both training and testing. The
variance and standard deviation of rainfall and PWP data in Model 2 used for training
are less than for its testing that indicates higher variability of rainfall and PWP data
used and it is expected Model 2 will experience greater loss of accuracy compared to
Model 1. Hence, this is proving the expected result of selection datasets earlier with
Model 1 is having better accuracy by 20.3% rather than Model 2.
.
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31
4.6.1 Model 1 Result Analysis and Discussion
Results from Model 1 is discussed here as it shows better result of R2 and MSE.
Based on PWP, Predicted PWP and Rainfall graph, the model able to show good
prediction as it predicts with small difference to observed values. This can relate to the
used of number of antecedent PWP and rainfall condition. According to Babangida et
al. (2016), the increase input features for rainfall antecedent demonstrate better result
up only to two antecedent records (ideal model features) as it yielded a small MSE
with considering computational ease and time factor. Beyond two antecedent records,
howbeit show only slight improvement compared to two antecedent records.
Nonetheless, addition of rainfall features solely does not significantly improve the
result. Number of PWP used improve the result as well with the limitation up to three
antecedent records. This is because, beyond three antecedent records will yield loss of
accuracy in predictions. Thus, features from one to three lag records able to provide
better modelling results as it decreases model complexity and computational burden
0
2
4
6
8
10
12
14
16
18
-11.3
-10.3
-9.3
-8.3
-7.3
-6.3
11/1/2014 11/2/2014 11/3/2014 11/4/2014 11/5/2014 11/6/2014 11/7/2014 11/8/2014 11/9/2014
PORE
WAT
ER P
RESS
URE
(KPA
)
DATE
PORE WATER PRESSURE, PREDICTED PORE WATER PRESSURE AND RAINFALL GRAPH
Observed PWP Predicted PWP Rainfall
Figure 12: Pore Water Pressure, Predicted Pore Water Pressure and Rainfall Graph
RAINFALL (m
m)
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32
that enhance improvement in accuracy. Therefore, Model 1 is having the most
optimum input patterns that promotes best accuracy.
The selection values of 1, 0.1, 0.001 and -1 for cost constant, gamma, epsilon
and Coefθ respectively give a good model combinations prediction as the values are
much closer to their respective default value. According to Raghavendra and Deka
(2014), smaller value of cost constant will cause the learning machine experiencing
poor approximation due to under fitting of training data whereas larger value of cost
constant will cause the training data overfits and making way for more complex
learning. For epsilon, its smaller value will yield complex learning machine while its
larger value will yield more flat estimated of the regression function. Hence, less
complex model is built with none of input features dominated one another.
However, number of Support Vector (nSV) in this study is showing more than
50% of the training set which tells over-fitting problem has occurred. This is reflected
what has been stated by Mattera and Haykin (1999) that nSV should be around half
the number of the training data points to avoid over-fitting problem. The higher value
of nSV will result a good accuracy during training but there was loss of accuracy
during testing. However, this is does not mean there is no good model with high
number of SVs, in fact number of SVs may largely depend on how well the data set is
structured (Babangida et al., 2016). Due to that, as for this study, the large number of
SVs might be happened due to a poorly structured and noisy data set used in the
process (Mattera and Haykin, 1999).
In addition, instead facing over-fitting problem and the model also showed the
difficulties to predict on extreme points as we can be seen on 5th November 2014 and
6th November 2014 in PWP, Predicted PWP and Rainfall graph. This can also be
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33
clearly illustrated as in following graph of extent of agreement between observed and
predicted PWP records;
PWP points on both 5th November 2014 and 6th November 2014 in the above
graph shows furthest from line of perfect fit. According Babangida et. al. (2016),
despite of rainfall, this extreme points are influenced by large temperature that exert
by movement of water vapor from high temperature region to low temperature region.
Hence it is quite difficult to predict extreme points accurately without the input of
temperature. Since fluctuation of PWP with temperature is not covered in this study,
nevertheless, the developed model able to show great promise in the prediction of PWP
by only using rainfall data. It can be readily used to overcome PWP fluctuation is short
period of time and thus, can be applied to slope management studies.
Figure 13: Extent of agreement between observed and predicted PWP records
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34
CONCLUSION AND RECOMMENDATION
Pore Water Pressure (PWP) as in general, is the indicator of the existence of
water filled the voids that exert external forces within the soil. By predicting the soil
PWP, one can know the possible condition of soil with particular external factors. The
model is successfully predicting PWP for 1 month of data with the usage of antecedent
PWP and antecedent rainfall alone without other influencing factor for example
evaporation, temperature and deep percolation. Despite of the difficulties to predict
extreme points accurately, the model shows a great promised in predict PWP. The
difficulties in predict extreme points are also influenced by other factor such as
temperature which is not significantly covered in this study. Hence, the technique used
in this study is able to solve PWP problems especially in the short period of time.
Model 1 yielded a better result compared to Model 2 with the statistical
measure of R-squared and MSE. Albeit the number of Support Vectors are more than
50% of total data points which tell loss of accuracy has occurred, it is most likely
caused by other influencing factors such as evaporation and deep percolation. Due to
that, the depth used in the instrumented slope might be too shallow for the failure plane
to exist. Thus, it is suggested to have a deeper regions prediction to be compared with
as in this study for future recommendation. Furthermore, instead of using only rainfall
data, prediction of PWP response towards climatic data such as evaporation also would
be interesting to be discovered.
Nevertheless, this study of demonstrating the capability of Sigmoid Kernel
Function to be used as tool to model PWP predictions is a successful and can be applied
for necessary safety measures to be taken towards slope failure and slope management
studies.
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35
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APPENDICES
Following is the used in the MATLAB software for both training and testing data
purposes. The codes originated same as in the study carried out by Babangida (2016).
Figure 14: Codes used in MATLAB software